STRONG CONSISTENCY UNDER GAUSS-MARKOV CONDITION

Authors
Citation
Xr. Chen et Mz. Jin, STRONG CONSISTENCY UNDER GAUSS-MARKOV CONDITION, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 39(2), 1996, pp. 137-147
Citations number
10
Categorie Soggetti
Multidisciplinary Sciences
ISSN journal
10016511
Volume
39
Issue
2
Year of publication
1996
Pages
137 - 147
Database
ISI
SICI code
1001-6511(1996)39:2<137:SCUGC>2.0.ZU;2-J
Abstract
Let Y-i=x(i)' beta+e(i), 1 less than or equal to i less than or equal to n, be a linear model, <(beta)over cap>(n)=(<(beta)over cap>(n1), .. ., <(beta)over cap>(np)) be the LS estimate of beta-(beta(1), ..., bet a(p))'. Denote by u(n) the (1,1)-element of [GRAPHICS] Assume that Ee( i)=0 and {e(i)} obeys the Gauss-Markov condition Ee(i)e(j)=sigma(2) de lta(ij). It is shown that [GRAPHICS] is a sufficient condition for <(b eta)over cap>(n1) to be strongly consistent. This condition is accurat e in the sense that for any e(n) --> 0, the condition[GRAPHICS] ceases to be sufficient. Some remarks are made concerning the necessary and/ or sufficient condition for <(beta)over cap>(n1) to be strongly consis tent.